Purity

This doesn’t affect her purity and she doesn’t have to make ghusul. She only needs to change and perform wudhu.

If they were in your pants, your prayers were valid and correct. But if it was on your underwear and it was dry sperm, then you should make ghusul and pray all the prayers again since you had woken up.

If the organs are all wet, she has to go back to what she missed and continue from there as the sequence must be followed.

He must wash his face and the skin underneath the beard if it is not heavy! If it is heavy, it is sufficient to put his wet fingers through it.

Yes.

Yes, you should wipe over the bun

When it is dry, it can’t be transferred unless it meets something wet or some of its mass is visibly seen on the other object.

Anything coming out of the private parts, except semen and also the blood of an animal slaughtered.

No problem and this is pure! What is not pure is the blood gushing from the animal when being slaughtered.

It doesn’t invalidate your wudhu unless you pass it out. You must suppress it.